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I don't know Lakka, but it appears to be in the hills behind Aegion. The road is a very minor road and terminates beyond Lakka, so you would have to return to near Aegion each time.

In Kalavryta there are a number of very nice (from the outside!) hotels and outside of the winter season they might be quite reasonably priced, certainly you could ask for a better price. Booking would not be necessary. There are also a few Hotels in Diakofto that look low priced.

Further up the coast towards Korinthos, 20 minutes from Aegion, 10 minutes from Diakofto, in Akrata there are two hotels, and a couple of apartment/rooms providers that again may be within your budget during May.

I seem to remember I only had success with Lemonies by using fax service.

( +30 6910 41820) & it was hard work as their English was about equal to my Greek!

No idea on Diakofto to Delphi as we have never travelled that route - perhaps Aredub might know . . . . . or you could do a route search on Michelin which will tell you the time, distance & any tolls payable.